Oposite type of predictions for unbalanced dataset
A random forest is a collection of classification trees. If more than 50% of these trees predict class A (and not class B), the random forest will predict class A. 

What you can do is lower the percentage needed to classify it as class A (in your case, patient has the virus). This way, you can tell your random forest to predict class A if only 20% (or 10%, or 5%, ...) of the decision trees actually predicts class A. 

I don't know what code you are using for the random forest algoritm, but in most you should be able to ask the % of certainty the random forest has of each class.